Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle

Naveed Ishtiaq Chaudhary,Zeshan Aslam Khan,Ahmad H Milyani,Khalid Mehmood Cheema,Muhammad Asif Zahoor Raja

doi:10.3390/math9243302

Abstract

Recently, a quasi-fractional order gradient descent (QFGD) algorithm was proposed and successfully applied to solve system identification problem. The QFGD suffers from the overparameterization problem and results in estimating the redundant parameters instead of identifying only the actual parameters of the system. This study develops a novel hierarchical QFDS (HQFGD) algorithm by introducing the concepts of hierarchical identification principle and key term separation idea. The proposed HQFGD is effectively applied to solve the parameter estimation problem of input nonlinear autoregressive with exogeneous noise (INARX) system. A detailed investigation about the performance of HQFGD is conducted under different disturbance conditions considering different fractional orders and learning rate variations. The simulation results validate the better performance of the HQFGD over the standard counterpart in terms of estimation accuracy, convergence speed and robustness.

Highlights

Fractional calculus has emerged as an important tool to effectively model a variety of systems or processes that arise in the various applications relating to physics, engineering and applied sciences [1,2,3,4,5,6,7,8]
In order to avoid the problem of overparameterization, we propose hierarchical quasi-fractional gradient (QFGD) (HQFGD) by integrating the hierarchical identification principle and key term separation idea with QFGD for efficient parameter estimation
Results of the proposed HQFGD are presented for parameter estimation

Summary

Introduction

Fractional calculus has emerged as an important tool to effectively model a variety of systems or processes that arise in the various applications relating to physics, engineering and applied sciences [1,2,3,4,5,6,7,8]. Liu et al generalized the GFGM to solve convex optimization problem with high dimensions, and proposed a quasi-fractional gradient (QFGD) method with theoretical analysis and convergence proof [36]. They applied QFGD to solve system identification problem through overparameterization and estimated the redundant parameters instead of estimating only the actual parameters of the system. In order to avoid the problem of overparameterization, we propose hierarchical QFGD (HQFGD) by integrating the hierarchical identification principle and key term separation idea with QFGD for efficient parameter estimation. We propose HQFGD method for efficient parameter estimation of input nonlinear autoregressive exogenous noise (INARX) systems

Methods

Results

Conclusion